The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Semiparametric Approach to Logistic Model with Random Intercept

준모수적 방법을 이용한 랜덤 절편 로지스틱 모형 분석

  • Kim, Mijeong (Department of Statistics, Ewha Womans University)
  • Received : 2015.11.24
  • Accepted : 2015.12.08
  • Published : 2015.12.31
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Abstract

Logistic models with a random intercept are useful to analyze longitudinal binary data. Traditionally, the random intercept of the logistic model is assumed to be parametric (such as normal distribution) and is also assumed to be independent to variables. Such assumptions are very strong and restricted for application to real data. Recently, Garcia and Ma (2015) derived semiparametric efficient estimators for logistic model with a random intercept without these assumptions. Their estimator shows the consistency where we do not assume any parametric form for the random intercept. In addition, the method is computationally simple. In this paper, we apply this method to analyze toenail infection data. We compare the semiparametric estimator with maximum likelihood estimator, penalized quasi-likelihood estimator and hierarchical generalized linear estimator.

의학이나 사회과학에서 이진 데이터 분석 시 랜덤 절편(random intercept)을 갖는 로지스틱 모형이 유용하게 쓰이고 있다. 지금까지는 이러한 로지스틱 모형에서 랜덤 절편이 정규분포와 같은 모수 모형(parametric model)을 따른다는 가정과 설명변수와 랜덤 절편이 독립이라는 가정 하에 실행된 데이터 분석이 전반적이었다. 그러나 이러한 두 가지 가정은 다소 무리가 있다. 이 연구에서는 설명 변수와 랜덤 절편의 독립성을 가정하지 않고, 비모수 랜덤 절편을 따르는 로지스틱 모형의 방법론을 기존에 널리 쓰인 방법과 비교하여 설명하도록 한다. 케냐의 초등학생들의 영양 섭취 및 질병의 발병을 조사한 데이터에 이 방법을 적용하였다.

Keywords

References

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